Least Common Multiple (LCM) of 113 and 186
The least common multiple (LCM) of 113 and 186 is 21018.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 113 and 186?
First, calculate the GCD of 113 and 186 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 186 = 0 remainder 113 |
| 2 | 186 ÷ 113 = 1 remainder 73 |
| 3 | 113 ÷ 73 = 1 remainder 40 |
| 4 | 73 ÷ 40 = 1 remainder 33 |
| 5 | 40 ÷ 33 = 1 remainder 7 |
| 6 | 33 ÷ 7 = 4 remainder 5 |
| 7 | 7 ÷ 5 = 1 remainder 2 |
| 8 | 5 ÷ 2 = 2 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 82 and 117 | 9594 |
| 97 and 194 | 194 |
| 119 and 77 | 1309 |
| 184 and 51 | 9384 |
| 93 and 128 | 11904 |